Pilearytix
A model of the brain's arousal system, November 2025 to March 2026
The locus coeruleus is a nucleus in the brainstem about the size of a grain of rice, and it sets how aroused the whole brain is by releasing noradrenaline into the cortex. I built this model of it between November 2025 and March 2026. Two settings run it, the level of noradrenaline and the balance between the nucleus's steady tonic firing and its sharp phasic bursts, and as you take them from coma through the optimum to collapse the eighty regions of the model's cortex brighten, dim and in the end go dark. Every number you can read off the page is either looked up in a simulation of 6,561 settings that I ran in neurolib or worked out live from the model's own gain equation.
Following Aston-Jones and Cohen (2005), I treated the level of noradrenaline as the arousal itself. There is no separate arousal variable in the model from which the noradrenaline is then worked out, because that would have been circular.
How the locus coeruleus fires
I modelled the nucleus as a single FitzHugh-Nagumo unit, a pair of equations in which v, standing in for the firing rate, is pulled back towards rest by a slower recovery variable w, and everything else on this page depends on what that unit puts out. With a steady moderate input it fires regularly, which is tonic firing, and with short strong pulses the same unit fires in bursts, which is phasic firing. Only the part of v above zero releases noradrenaline into the cortex.
dv/dt = v β vΒ³/3 β w + I
dw/dt = (v + a β bΒ·w) / Ο
Here a is 0.7, b is 0.8 and Ο is 12.5, and the input I is held at 0.65 for tonic firing or pulsed to 1.5 for phasic.
Turning the noradrenaline up and down
The dashed line is the inverted U the model is built on (Arnsten 2011), in which noradrenaline raises the cortex's gain up to an optimum at 0.5, brings it back to zero at 0.8 and turns it negative beyond that, and over it I've drawn in solid blue the mean excitation my simulation actually produced at the current tonic-phasic setting, stretched to fill the height of the chart. That blue line jumps about from one setting to the next and never peaks at 0.5, so the model doesn't reproduce the curve it was built on, and before it is stretched it moves by only about two hertz across the whole sweep.
Drag along the curve, move the sliders or pick a state or a clinical profile along the top of the box, and the map of the cortex, the figure and its seven readouts change with the model. A state or a profile puts the model straight at the place I gave it, and a drug moves it from wherever it is by the step I gave that drug. I chose every one of those places and steps by hand, on top of receptor maps that were measured, so none of them is a clinical finding.
Hover a cell to read it, and click to move the model there.
Loading the sweepβ¦
eighty regions of the cortex, from above
the figure and its seven readouts
Each dot on the map is a region of the AAL2 atlas, with the left hemisphere on the left. A dot is larger where the region holds more of the noradrenaline transporter and darker where its hemisphere's gain multiplied by that density is higher, and it turns into a red ring once the gain goes negative. Hover a dot for its name and its network.
Drawn as every setting at once, the two settings make a plane, with noradrenaline up the side and the tonic-phasic balance along the bottom, taken down to 41 by 41 from the grid of 81 by 81 settings I ran in neurolib with the cortex feeding back into the locus coeruleus. Each measure is stretched so that its own lowest value is pale and its highest dark, because the raw values barely vary.
Arousal sets how fast the figure breathes and how upright it sits, sustained attention how steadily it holds its gaze, selective attention the width of its pupils, cognitive control whether it moves smoothly or in jerks, sensory reactivity how often it flinches, emotional regulation its brows and mouth, and network stability whether its outline holds together or splits into offset copies of itself.
The readouts are each scaled from 0 to 1, the left hemisphere in blue and the right in green. The two columns differ even when both sides get the same noradrenaline, because each hemisphere is wired differently in the connectome, and across the whole sweep the right scores higher on arousal, which agrees with the mostly right-hemisphere network for alertness that imaging studies have found (Sturm and Willmes 2001). The left scores higher on sustained attention and network stability. Hover a name for what it measures.
Where the model goes flat
Across all 6,561 settings the mean excitation of the cortex stays between 18.25 and 20.40 Hz. At noradrenaline 0.10 and below the model returns exactly 18.273 Hz whatever the tonic-phasic balance, as do some settings up to about 0.23 and a handful further up the curve, so that of the 1,406 settings in the lowest bin of the histogram 1,022 are exactly 18.273 Hz.
Reduced to these two settings the model is mostly a plateau with a few cliffs in it, and most of the movement in the instrument above comes from stretching the line and from the seven readouts worked out from the simulation. The readout I named arousal moves only between 2.07 and 2.27 anywhere in the sweep, a range of two tenths on a scale where its neighbour, selective attention, runs from 0 to 4.2.
Where the numbers come from
Each region responds to noradrenaline in its own way because the model weights it by nineteen receptor and transporter densities that Hansen and colleagues measured with PET across 1,238 people (2022), so the regions densest in the noradrenaline transporter move furthest when the setting changes. Those maps are the one part of the model that comes from measurement. The model covers the cortex alone, eighty regions of the AAL2 atlas grouped into the seven Yeo networks, and leaves out the thalamus, the striatum, the amygdala and the rest of the subcortex.
The nineteen maps cover nine systems: noradrenaline through its transporter, NET, which stands in for how densely the locus coeruleus reaches each region; dopamine through D1, D2 and its transporter, for prefrontal drive that rises and falls through D1 and rises steadily through D2; serotonin through six maps (5-HT1A, 1B, 2A, 4, 6 and the transporter), which inhibit limbic cortex and excite sensory cortex; acetylcholine through Ξ±4Ξ²2, M1 and VAChT, which raise the gain of attention; glutamate through mGluR5 and NMDA for the main excitatory drive; GABA through GABAa as the brake on excitation; histamine through H3 for wakefulness; and the cannabinoid CB1 and opioid MOR maps, which enter as a term in network stability and as a weight on affect.
On top of the maps sit roughly 120 constants that I set by hand and listed in the project's optimisation notes. Eleven shape the gain curve, among them the optimum at 0.5 and the 0.3 width of its falling side, and eighteen belong to the oscillator and the terms around it. Fifty-seven are the weights that turn seven networks into seven readouts and let the receptors modulate each one, and they decide whether the presets come out different from one another at all. The last thirty-three set reference ranges, score ranges and how fast the receptors desensitise. Nearly all of them were chosen to keep the numbers stable, and the positions of the presets are defaults I chose to illustrate, which no paper supplied.
I've half-built a plan to fit these constants against real neuroimaging data, the way the second model below was fitted, so that an optimiser can show which of my guesses were wrong. Until then the model is a measured receptor map with a stack of plausible coefficients on top and a single noradrenaline setting doing most of the work.
A second model, from development to diagnosis
The second model is a developmental cascade that I first built as a hand-tuned spreadsheet and then fitted with nc-model-ml, training code I wrote for it. Its 51 free inputs, which cover genes, counts of neural-crest cells, neurotransmitter tone, environment and medication, feed 157 DSM criteria and through them 17 diagnosis loads, and its weights were learned from the ABIDE and ADHD-200 cohorts. I ported the whole computation to JavaScript, so moving a slider re-evaluates all 304 of its formulas in your browser, and the page checks the port against the original model as it loads.
This is a research model and can't diagnose anyone. The bars are the model's own outputs reproduced in JavaScript, and they say nothing clinical about any person.
the 51 developmental inputs
predicted diagnosis loads
From 0 to 1, red above 0.50. Hover a name for its full title.
worked out inside the cascade
The second model at the first model's setting
Here the developmental cascade runs with neurotypical defaults for every input except the three it shares with the arousal model, the noradrenaline tone of each hemisphere and the tonic-phasic mode, which follow the settings in the instrument further up. A moment's arousal has no developmental history behind it, so this says nothing about a real person. It is the cascade's response when those three inputs move and everything else stays neutral, and at the resting setting it gives the neurotypical result unchanged.
Loading the second modelβ¦
The cohorts it was fitted to
I fitted the second model's weights to two public collections of brain scans that come with research diagnoses, the Autism Brain Imaging Data Exchange (ABIDE I and II) and the ADHD-200 sample, 2,424 subjects in all, and tested each training run on between 250 and 274 subjects held back from its training. The fit I use on this page tells autistic subjects from controls with an AUROC of 0.89, where 0.5 is chance and 1 is perfect, and its predictions correlate with clinical severity at r = 0.90. The best single runs reached 0.96 and 0.94.
Each run was tested on only 250 to 274 subjects, no single run has both the highest AUROC and the highest correlation with severity, and the labels are the research diagnoses these studies made. A mechanistic developmental cascade can separate real cohorts this far, and it would need a great deal more testing before it could screen anyone.
Training runs
Hover or tap a run to read it.
600 real subjects
Hover or tap a point to read it.
Subjects with no severity score are left out.
Four subtypes
Four clusters found in the fitted data. The long bar under each is its mean severity out of 10, and each of the small bars is one input, drawn in blue above the line where the subtype sits above the population's mean and in red below it where it sits below.
How I built it
The arousal model has eighty cortical regions from the AAL2 atlas, joined by a connectome from the Human Connectome Project's diffusion imaging and simulated with neurolib's adaptive linear-nonlinear mass model, with a FitzHugh-Nagumo oscillator for each hemisphere's locus coeruleus coupled across the midline. I drew every chart on this page myself in SVG and canvas, from a 41 by 41 downsample of the sweep that weighs 290 KB.
The brightness of each region is worked out live from the model's gain equation, uΒ·NETΒ·0.5 + tpΒ·uΒ·NETΒ², where u is the height of the inverted U and NET is the region's transporter density. The readouts, the map of every setting, the histogram and the readings at each preset are all looked up in the sweep.
I call this way of working algorithmic frottage, a rubbing taken from a statistical model of a mind, and like any rubbing it picks up the flat stretches too.
References
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Arnsten, Scahill & Findling (2007). Ξ±2-adrenergic receptor agonists for the treatment of attention-deficit/hyperactivity disorder: emerging concepts from new data. Journal of Child and Adolescent Psychopharmacology 17, 393β406.
Aston-Jones & Cohen (2005). An integrative theory of locus coeruleus-norepinephrine function: adaptive gain and optimal performance. Annual Review of Neuroscience 28, 403β450.
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Meyer et al. (2004). Serotonin transporter occupancy of five selective serotonin reuptake inhibitors at different doses: an [11C]DASB positron emission tomography study. American Journal of Psychiatry 161, 826β835.
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